Rapid reduced-order inverse design method for three-dimensional curved shock

In a hypersonic field, precise shock control is critical for waverider and inlet design. Conventional osculating axisymmetric theory effectively handles conical shocks; however, it is challenging to apply directly to the inverse design of three-dimensional (3D) shocks, especially when it fails to account for circumferential flow effects. To overcome the shortcomings of the osculating axisymmetric theory, this paper proposed a reduced-order inverse design method for 3D shocks, with the core of this method being a grid node solving algorithm called the circumferential gradient-coupled method of characteristics with Swirl (CGC-MOCS). The complete detail of the CGC-MOCS algorithm and the inverse design method for 3D shocks are presented. Additionally, this method has also been successfully applied to the design of waveriders. The numerical simulation demonstrates remarkable accuracy in the reconstruction of variable cross section elliptical shock, with computational fluid dynamic results showing excellent agreement with within 3.4% maximum wall pressure deviation. For the waverider configuration, the method maintains consistently high fidelity, limiting errors to just 2.3% in wall pressure and 2.2% in lift-to-drag ratio performance. These results demonstrate that the inverse design methodology of 3D shock can accurately reproduce the target shock structure, exhibit excellent adaptability to complex 3D flow effects, and indicate significant potential for engineering applications in hypersonic propulsion technology.